Template:Intmath/testcases
- Script error: No such module "Purge".
Note: the {{intmath/sandbox}} code is tweaked and/or optimized for use inside the {{math}} template.
In IE, except for int, all the integrals seem to render in the beautiful font 'Lucida Sans Unicode', but in Firefox we get this ugly font (it is passable for text style, but would be really ugly in display style)! In which [ugly] font do the integral symbols, other than int, render? Also, in which font does int render? — TentaclesTalk or ✉ mailto:Tentacles 17:50, 22 March 2016 (UTC)
Contents
No {{math}}
Compare vertical alignment and obliqueness of [rotated] int with other [italic] integral symbols:
- ∫
∯
∫
{{intmath/sandbox|int}} <!-- 1 hair space -->{{intmath/sandbox|oiint}} <!-- 1 hair space -->{{intmath/sandbox|int}}
Gamma function (non-italic int as default)
- Sandbox Γ(z) = ∫∞
0 e−t t z − 1dt - Current Γ(z) = ∫∞
0 e−t t z − 1dt
Γ(''z'') = {{intmath||0|∞}} ''e''<sup>−''t''</sup> <!-- hair space -->''t'' <!-- hair space --><sup>''z'' <!-- hair space -->− <!-- hair space -->1</sup>''dt''
- Sandbox Γ(z) = ∫∞
0 e−t t z − 1dt - Current Γ(z) = ∫∞
0 e−t t z − 1dt
Γ(''z'') = {{intmath|int|0|∞}} ''e''<sup>−''t''</sup> <!-- hair space -->''t'' <!-- hair space --><sup>''z'' <!-- hair space -->− <!-- hair space -->1</sup>''dt''
- Sandbox ∲
C F(x) ∙ dx = −∳
C F(x) ∙ dx - Current ∲
C F(x) ∙ dx = −∳
C F(x) ∙ dx
{{intmath|varointclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x''' = −{{intmath|ointctrclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x'''
Sandbox
- Gauss's law ∯
∂Ω E ∙ dS = Template:Sfrac∭
Ω ρ dV - Gauss's law for magnetism ∯
∂Ω B ∙ dS = 0 - Maxwell–Faraday equation ∮
∂Σ E ∙ dℓ = −∬
Σ Template:Sfrac ∙ dS - Ampère's circuital law ∮
∂Σ B ∙ dℓ = ∬
Σ (μ0J + Template:SfracTemplate:Sfrac) ∙ dS
Current
- Gauss's law ∯
∂Ω E ∙ dS = Template:Sfrac∭
Ω ρ dV
- Gauss's law for magnetism ∯
∂Ω B ∙ dS = 0
- Maxwell–Faraday equation ∮
∂Σ E ∙ dℓ = −∬
Σ Template:Sfrac ∙ dS
- Ampère's circuital law ∮
∂Σ B ∙ dℓ = ∬
Σ (μ0J + Template:SfracTemplate:Sfrac) ∙ dS
{{intmath|oiint|∂Ω}} '''E''' ∙ ''d'''''S''' = {{sfrac|1|''ε''<sub>0</sub>}}{{intmath|iiint|Ω}} ''ρ'' ''dV''
{{intmath|oiint|∂Ω}} '''B''' ∙ ''d'''''S''' = 0
{{intmath|oint|∂Σ}} '''E''' ∙ ''d''<nowiki />'''''ℓ<!-- ℓ -->''''' = −{{intmath|iint|Σ}} {{sfrac|∂'''B'''|∂''t''}} ∙ ''d'''''S'''
{{intmath|oint|∂Σ}} '''B''' ∙ ''d''<nowiki />'''''ℓ<!-- ℓ -->''''' = {{intmath|iint|Σ}} (''μ''<sub>0</sub>'''J''' + {{sfrac|1|''c''<sup>2</sup>}}{{sfrac|∂'''E'''|∂''t''}}) ∙ ''d'''''S'''
{{math}}
Compare vertical alignment and obliqueness of [rotated] int with other [italic] integral symbols:
- ∫
∯
∫
{{math| {{intmath/sandbox|int}} <!-- 1 hair space -->{{intmath/sandbox|oiint}} <!-- 1 hair space -->{{intmath/sandbox|int}} }}
Gamma function (non-italic int as default)
- Sandbox Γ(z) = ∫∞
0 e−t t z − 1dt - Current Γ(z) = ∫∞
0 e−t t z − 1dt
{{math|Γ(''z'') {{=}} {{intmath||0|∞}} ''e''<sup>−''t''</sup> <!-- hair space -->''t'' <!-- hair space --><sup>''z'' <!-- hair space -->− <!-- hair space -->1</sup>''dt''}}
- Sandbox Γ(z) = ∫∞
0 e−t t z − 1dt - Current Γ(z) = ∫∞
0 e−t t z − 1dt
{{math|Γ(''z'') {{=}} {{intmath|int|0|∞}} ''e''<sup>−''t''</sup> <!-- hair space -->''t'' <!-- hair space --><sup>''z'' <!-- hair space -->− <!-- hair space -->1</sup>''dt''}}
- Sandbox ∲
C F(x) ∙ dx = −∳
C F(x) ∙ dx - Current ∲
C F(x) ∙ dx = −∳
C F(x) ∙ dx
{{math|{{intmath|varointclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x''' {{=}} −{{intmath|ointctrclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x'''}}
Sandbox
- Gauss's law ∯
∂Ω E ∙ dS = Template:Sfrac∭
Ω ρ dV
- Gauss's law for magnetism ∯
∂Ω B ∙ dS = 0
- Maxwell–Faraday equation ∮
∂Σ E ∙ dℓ = −∬
Σ Template:Sfrac ∙ dS
- Ampère's circuital law ∮
∂Σ B ∙ dℓ = ∬
Σ (μ0J + Template:SfracTemplate:Sfrac) ∙ dS
Current
- Gauss's law ∯
∂Ω E ∙ dS = Template:Sfrac∭
Ω ρ dV
- Gauss's law for magnetism ∯
∂Ω B ∙ dS = 0
- Maxwell–Faraday equation ∮
∂Σ E ∙ dℓ = −∬
Σ Template:Sfrac ∙ dS
- Ampère's circuital law ∮
∂Σ B ∙ dℓ = ∬
Σ (μ0J + Template:SfracTemplate:Sfrac) ∙ dS
{{math|{{intmath|oiint|∂Ω}} '''E''' ∙ ''d'''''S''' {{=}} {{sfrac|1|''ε''<sub>0</sub>}}{{intmath|iiint|Ω}} ''ρ'' ''dV''}}
{{math|{{intmath|oiint|∂Ω}} '''B''' ∙ ''d'''''S''' {{=}} 0}}
{{math|{{intmath|oint|∂Σ}} '''E''' ∙ ''d''<nowiki />'''''ℓ<!-- ℓ -->''''' {{=}} −{{intmath|iint|Σ}} {{sfrac|∂'''B'''|∂''t''}} ∙ ''d'''''S'''}}
{{math|{{intmath|oint|∂Σ}} '''B''' ∙ ''d''<nowiki />'''''ℓ<!-- ℓ -->''''' {{=}} {{intmath|iint|Σ}} (''μ''<sub>0</sub>'''J''' + {{sfrac|1|''c''<sup>2</sup>}}{{sfrac|∂'''E'''|∂''t''}}) ∙ ''d'''''S'''}}
Display style standalone formulae
{{Bigmath}}
Compare vertical alignment and obliqueness of [rotated] int with other [italic] integral symbols:
- ∫
∯
∫
{{Bigmath| {{intmath/sandbox|int}} <!-- 1 hair space -->{{intmath/sandbox|oiint}} <!-- 1 hair space -->{{intmath/sandbox|int}} }}
LaTeX
The Gamma function is defined as
- <math>\Gamma(z) = \int_0^\infty e^{-t} t^{z-1} \, dt.</math>
Sandbox
The Gamma function is defined as
- Γ(z) = ∫∞
0 e−t t z − 1dt.
Current
The Gamma function is defined as
- Γ(z) = ∫∞
0 e−t t z − 1dt.
{{Bigmath|Γ(''z'') {{=}} {{intmath|int|0|∞}} ''e''<sup>−''t''</sup> <!-- hair space -->''t'' <!-- hair space --><sup>''z'' <!-- hair space -->− <!-- hair space -->1</sup>''dt''.}}
LaTeX
Gauss's law:
Gauss's law for magnetism:
Maxwell–Faraday equation:
- <math>\oint_{\partial \Sigma} \mathbf{E} \cdot d\boldsymbol{\ell} = - \iint_{\Sigma} \frac{\partial \mathbf{B}}{\partial t} \cdot d\mathbf{S} </math>
Ampère's circuital law:
- <math>\oint_{\partial \Sigma} \mathbf{B} \cdot d\boldsymbol{\ell} = \iint_{\Sigma} \left( \mu_0 \mathbf{J} + \frac{1}{c^2} \frac{\partial \mathbf{E}}{\partial t} \right) \cdot d\mathbf{S} </math>
Sandbox
Gauss's law:
- ∯
∂Ω E ∙ dS = Template:Sfrac∭
Ω ρ dV
Gauss's law for magnetism:
- ∯
∂Ω B ∙ dS = 0
Maxwell–Faraday equation:
- ∮
∂Σ E ∙ dℓ = −∬
Σ Template:Sfrac ∙ dS
Ampère's circuital law:
- ∮
∂Σ B ∙ dℓ = ∬
Σ (μ0J + Template:SfracTemplate:Sfrac) ∙ dS
Current
Gauss's law:
- ∯
∂Ω E ∙ dS = Template:Sfrac∭
Ω ρ dV
Gauss's law for magnetism:
- ∯
∂Ω B ∙ dS = 0
Maxwell–Faraday equation:
- ∮
∂Σ E ∙ dℓ = −∬
Σ Template:Sfrac ∙ dS
Ampère's circuital law:
- ∮
∂Σ B ∙ dℓ = ∬
Σ (μ0J + Template:SfracTemplate:Sfrac) ∙ dS
Gauss's law: :{{Bigmath|{{intmath|oiint|∂Ω}} '''E''' ∙ ''d'''''S''' {{=}} {{sfrac|1|''ε''<sub>0</sub>}}{{intmath|iiint|Ω}} ''ρ'' ''dV''}}
Gauss's law for magnetism: :{{Bigmath|{{intmath|oiint|∂Ω}} '''B''' ∙ ''d'''''S''' {{=}} 0}}
Maxwell–Faraday equation: :{{Bigmath|{{intmath|oint|∂Σ}} '''E''' ∙ ''d''<nowiki />'''''ℓ<!-- ℓ -->''''' {{=}} −{{intmath|iint|Σ}} {{sfrac|∂'''B'''|∂''t''}} ∙ ''d'''''S'''}}
Ampère's circuital law: :{{Bigmath|{{intmath|oint|∂Σ}} '''B''' ∙ ''d''<nowiki />'''''ℓ<!-- ℓ -->''''' {{=}} {{intmath|iint|Σ}} {{big|(}}''μ''<sub>0</sub>'''J''' + {{sfrac|1|''c''<sup>2</sup>}}{{sfrac|∂'''E'''|∂''t''}}{{big|)}} ∙ ''d'''''S'''}}
\iiiint and \idotsint
LaTeX
<math>H {{=}} \iiiint_{\rm 4\mbox{-}ball} dH</math> yields
- <math>H = \iiiint_{\rm 4\mbox{-}ball} dH</math>
<math>H {{=}} \idotsint_{n{\rm \mbox{-}ball}} dH</math> yields
- <math>H = \idotsint_{n{\rm \mbox{-}ball}} dH</math>
<math>H {{=}} \int \cdots \int_{n{\rm \mbox{-}ball}} dH</math> yields
- <math>H = \int \cdots \int_{n{\rm \mbox{-}ball}} dH</math>
<math>H {{=}} \int \!\cdots\! \int_{n{\rm \mbox{-}ball}} dH</math> yields (the better spaced)
- <math>H = \int \!\cdots\! \int_{n{\rm \mbox{-}ball}} dH</math>
HTML
{{math| H {{=}} {{intmath/sandbox|iiiint|4-ball}} ''dH'' }} yields the HTML text style H = ⨌
4-ball dH
{{math| H {{=}} {{intmath/sandbox|idotsint|''n''-ball}} ''dH'' }} yields the HTML text style H = ∫
⋯ ∫
n-ball dH
{{bigmath| H {{=}} {{intmath/sandbox|iiiint|4-ball}} ''dH'' }} yields the HTML display style
- H = ⨌
4-ball dH
{{bigmath| H {{=}} {{intmath/sandbox|idotsint|''n''-ball}} ''dH'' }} yields the HTML display style
- H = ∫
⋯ ∫
n-ball dH
Quotient of integrals
LaTeX
<math>\frac{ \int_0^\infty x^{2n} e^{-a x^2}\,dx }{ \int_0^\infty x^{2(n-1)} e^{-a x^2}\,dx } = \frac{2n-1}{2a}</math> yields
- <math>\frac{ \int_0^\infty x^{2n} e^{-a x^2}\,dx }{ \int_0^\infty x^{2(n-1)} e^{-a x^2}\,dx } = \frac{2n-1}{2a}</math>
HTML sandbox
:{{bigmath|<!--
-->{{sfrac
| {{intmath/sandbox|int|0|∞}} ''x''<sup>2''n''</sup> ''e''<sup>−''ax''<sup>2</sup></sup> ''dx''<!--
-->| {{intmath/sandbox|int|0|∞}} ''x''<sup>2(''n''−1)</sup> ''e''<sup>−''ax''<sup>2</sup></sup> ''dx''<!--
-->}} {{=}} {{sfrac|2''n'' − 1|2''a''}}
}}
yields (should I create a tint option to get a tiny integral?)
HTML sandbox (testing extra code for tiny integral)
:{{bigmath|
<div style{{=}}"vertical-align: middle;"><!--
-->{{sfrac
| <span style{{=}}"font-size: 0.75em; vertical-align: 0.3em;">{{intmath/sandbox|int|0|∞}}</span> ''x''<sup>2''n''</sup> ''e''<sup>−''ax''<sup>2</sup></sup> ''dx''<!--
-->| <span style{{=}}"font-size: 0.75em; vertical-align: 0.3em;">{{intmath/sandbox|int|0|∞}}</span> ''x''<sup>2(''n''−1)</sup> ''e''<sup>−''ax''<sup>2</sup></sup> ''dx''<!--
-->}} {{=}} {{sfrac|2''n'' − 1|2''a''}}
</div>
}}
yields (should I create a tint option to get a tiny integral?) ({{bigmath}} should have vertical-align: middle;)
HTML current
:{{bigmath|<!--
-->{{sfrac
| {{intmath|int|0|∞}} ''x''<sup>2''n''</sup> ''e''<sup>−''ax''<sup>2</sup></sup> ''dx''<!--
-->| {{intmath|int|0|∞}} ''x''<sup>2(''n''−1)</sup> ''e''<sup>−''ax''<sup>2</sup></sup> ''dx''<!--
-->}} {{=}} {{sfrac|2''n'' − 1|2''a''}}
}}
yields